Medieval Islamic warriors during the period of the Crusades used straight-bladed swords as well. It's something of a myth that straight-bladed swords are "infantry" weapons while curved ones are "cavalry" weapons. Many warriors from all over the world have used one or the other in both roles. Until professional standing armies start to arise in the early modern period, it's useless to draw a hard line between infantry and cavalry anyways. Despite the bluster of 19th century swordsmanship manuals furiously debating the issue of cut vs thrust, there never was and never will be a "best" sword design. There's simply too many variables at play on the battlefield to ascribe victories and defeats to something as relatively minor as the shape of a particular sword.